Large aperture super wide angle lens

ABSTRACT

A super wide angle lens system consisting of thirteen lenses grouped in eleven lens components wherein the following conditions (1) to (6) are satisfied: 
     
         F/0.75 &lt;|F.sub.1.2 |&lt;F/0.45, F.sub.1.2 &lt;0 1. 
    
     
         f/0.32 &lt;|f.sub.1.2.3 |&lt;f/0.18, f.sub.1.2.3 &lt;0 2. 
    
     
          0.8 &lt;f/f.sub.6 &lt;2.5                                       3. 
    
     
          0.4F &lt;d.sub.17 &lt;0.7F F                                    4. 
    
     
          1.2f &lt;r.sub.20 &lt;1.8F, 1.75 &lt;n.sub.11                      5. 
    
     
          58 &lt; ( ν.sub.10 + ν.sub.12 + ν.sub.13) / 3 &lt; 71.  6.

SUMMARY OF THE INVENTION

As the development of wide angle lenses advance, a small and largeaperture retrofocus type super wide angle lens has become a principledesign objective. The present invention relates to a comparatively largeaperture lens of this type, and more specifically to a super wide anglelens system consisting of 13 lenses grouped in 11 lens componentswherein the following conditions (1) to (6) are satisfied:

     F/0.75 <|F.sub.1.2 |<F/0.45, F.sub.1.2 < 0 1.

     f/0.32 <|f.sub.1.2.3 |<f/0.18, f.sub.1.2.3 < 0 2.

     0.8 <f/f.sub.6 <1.5                                       3.

     0.4F <d.sub.17 <0.7F                                      4.

     1.2f <r.sub.20 <1.8F,                                     5.

1.75 < n₁₁

     58 < (ν.sub.10 + ν.sub.12 + ν.sub.13) /3 < 71.   6.

BRIEF DESCRIPTION OF THE DRAWINGS

The specific nature of the invention, as well as other objects, aspects,uses and advantages thereof, will clearly appear from the followingdescription and from the accompanying drawings, in which:

FIG. 1 is a view showing the lens system in accordance with the firstembodiment of the invention including a filter,

FIGS. 2a to 2d show aberration curves obtained by the lens system inaccordance with the first embodiment of the invention,

FIG. 3 is a view showing the lens system in accordance with the secondembodiment of the invention including a filter, and

FIGS. 4a to 4d show aberration curves obtained by the lens system inaccordance with the second embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Describing the construction of the lens first, the first and the secondlenses are negative meniscus lenses convex to the object. The third lensis a positive lens, and the fifth, sixth and seventh lenses are cementedtogether. The fourth lens is a negative meniscus lens located betweenthe third and the fifth lenses and convex to the object similarly to thefirst and the second meniscus lenses. The fifth and the seventh lensesare negative lenses and cemented to the both surfaces of the sixthbiconvex lens. The eighth lens is a negative meniscus lens convex to theobject, and a filter is located therebehind. (The position of the filteris, however, not limited to between the eighth and ninth lenses.) Behindthe filter is located the ninth positive lens. A comparatively thicktenth positive lens is located behind the ninth lens, and a negativeeleventh lens is located therebehind. The twelfth and the thirteenthlenses are positive lenses located so that the greater curvature sidethereof face the image.

Now the conditions to be satisfied will be described in detail. Thereference characters designate the following factors:

F: composite focal length of the whole lens system

F₁.2. . . . i : composite focal length of the lens system consisting ofthe first to the i-th lenses

n_(i) : refractive index for d-line of the i-th lens

r_(j) : radius of curvature of the j-th face

ν _(i) : Abbe's number of the i-th lens

d_(k) : k-th lens thickness or spacing

f_(i) : focal length of the i-th lens.

The conditions are as follows:

     F/0.75 <|F.sub.1.2 |< F/0.45, F.sub.1.2 < 0 1.

     f/0.32<|f.sub.1.2.3 |< f/0.18, f.sub.1.2.3 < 0 2.

     0.8<f/f.sub.6 < 1.5                                       3.

    0.4F< d.sub.17 <0.7F                                       4.

    1.2f < r.sub.20 < 1.8F,                                    5.

1.75 < n₁₁

    58 < (ν .sub.10 +ν.sub.12 +ν.sub.13)/3 < 71.      6.

The first condition (1) defines the composite focal length of the frontlens component in order to obtain a long back focal length. In order toobtain a large aperture and wide angle lens, the front lens component ismade to consist of two negative meniscus lenses. By using two meniscuslenses, the degradation of the aberration occuring when only one lens isused is prevented. If the focal length |F₁.2 | becomes shorter thanF/0.75, the aberration is increased. This means that the glass used forthe second lens must have a comparatively high refractive index. If thefocal length |F₁.2 | becomes longer than F/0.45, the back focus cannotbe obtained and it becomes unnecessary to use two lenses foraccomplishing the desired effect.

The second condition (2) defines the focal length of the third lensprovided for correcting the distortion. If the focal length F₁.2.3becomes longer than F/0.18, the first (1) condition becomes difficult tosatisfy, whereas the distortion is well corrected. If the focal lengthbecomes shorter than F/0.32, it becomes difficult to make the sixth facework effectively without lowering the effect of preventing distortion.

The third condition (3) defines the power of the sixth lens to properlycorrect the chromatic aberration and balances the coma aberration andprevent the increase in the spherical aberration. Although thiscondition is concerned with the radius of curvature as well as thechromatic aberration, the main purpose of this condition is related tothe power of the sixth lens. When F/f₆ is smaller than 0.8, thecorrection of chromatic aberration becomes insufficient, and thespherical aberration must be partly corrected by other lenses, whichresults in an increase in aberration. In addition, the coma aberrationis imbalanced, and the aberration is enlarged in the field of wideangles. To the contrary, when the ratio F/f₆ becomes larger than 1.5,lenses are loaded with a reversely effecting burden to correctaberrations particularly to correct the coma aberration.

The fourth condition (4) defines the thickness of the tenth lens tocorrect the coma aberration in association with the fifth condition (5).When the thickness is larger than 0.7F, the amount of light becomesinsufficient or the rear lens component is required to be large althoughthe coma is sufficiently corrected. When the thickness is smaller than0.4F, the coma is not corrected sufficiently and it becomes difficult toobtain a large aperture lens system because the fifth condition ishardly corrected.

The fifth condition (5) defines the radius of curvature of the rear faceof the eleventh lens and the refractive index of the glass thereof inorder to correct the coma aberration. Particularly, the light incidentto the lens system at a comparatively small angle is influenced by thiscondition. The condition that n₁₁ is larger than 1.75 is indispensablefor determining the radius of curvature r₂₀ in consideration of thebalance of chromatic aberration in the rear lens component. When n₁₁ issmaller than 1.75, the radius of curvature r₂₀ becomes too small andaccordingly the coma aberration is degraded. Under the above condition,when r₂₀ becomes longer than 1.8F, the aberration increases in theopposite side and it becomes difficult to correct the increasedaberration.

The sixth condition (6) are indispensable for correction of thechromatic aberrations in the rear lens component. If the mean value ofthe Abbe's number is smaller than 58, the power of the eleventh lensmust be increased or the number of lenses must be increased. If thepower is increased, the coma aberration is degraded as in the fifthcondition. The number of lenses is naturally desired to be as small aspossible.

Two specific examples of the present invention will be describedhereinbelow.

The first example is shown in FIG. 1 and consists of first and secondnegative mensicus lenses L₁ and L₂ convex to the object, a positive lensL₃, a negative meniscus lens L₄ which, like lenses L₁ and L₂, is convexto the object, a cemented triplet consisting of negative lenses L₅ andL₇ cemented to opposite surfaces of a biconvex lens L₆, a negativemeniscus lens L₈ convex to the object, a positive lens L₉, acomparatively thick positive lens L₁₀, a negative lens L₁₁, and positivelenses L₁₂ and L₁₃ both of which are convex to the image. A filter islocated between lenses L₈ and L₉, although the position of the filter isnot critical. The radii r₁ to r₂₄ and the thicknesses and separations d₁to d₂₃, along with the refractive indices n₁ to n₁₃ and Abbe numbers ν ₁to ν₁₃ for lenses L₁ to L₁₃ are given in Table 1 as follows:

F = 100

F₁.2 = 171.5

F₁.2.3 = -401.4

f₆ = 82.5

                                      TABLE 1                                     __________________________________________________________________________         Radius of Curva-                                                                        Lens Thickness                                                                            Refractive                                                                            Abbe                                       Lens ture r    or Distance d                                                                             Index n No. ν                                   __________________________________________________________________________         r.sub.1 = 256.3                                                          L.sub.1        d.sub.1 = 6.5                                                                             n.sub.1 = 1.6031                                                                      ν.sub.1 = 60.7                               r.sub.2 = 121.6                                                                         d.sub.2 = 47.4                                                      r.sub.3 = 253.9                                                          L.sub.2        d.sub.3 = 14.1                                                                            n.sub.2 = 1.7410                                                                      ν.sub.2 = 52.7                               r.sub.4 = 125.8                                                                         d.sub.4 = 57.4                                                      r.sub.5 = 783.8                                                          L.sub.3        d.sub.5 = 22.9                                                                            n.sub.3 = 1.6258                                                                      ν.sub.3 = 35.7                               r.sub.6 =-430.9                                                                         d.sub.6 = 6.1                                                       r.sub.7 = 211.3                                                          L.sub.4        d.sub.7 = 9.3                                                                             n.sub.4 = 1.8160                                                                      ν.sub.4 =  46.8                              r.sub.8 = 119.7                                                                         d.sub.8 = 16.4                                                      r.sub.9 = 277.8                                                          L.sub.5        d.sub.9 = 8.1                                                                             n.sub.5 = 1.5473                                                                      ν.sub.5 = 53.6                               r.sub.10 = 119.3                                                         L.sub.6        d.sub.10 = 43.2                                                                           n.sub.6 = 1.7200                                                                      ν.sub.6 = 50.3                               r.sub.11 =-100.4                                                         L.sub.7        d.sub.11 = 12.6                                                                           n.sub.7 = 1.5613                                                                      ν.sub.7 = 45.2                               r.sub.12 = 5113.5                                                                       d.sub.12 = 0.5                                                      r.sub.13 = 89.6                                                          L.sub.8                                                                            d.sub.13 = 8.1                                                                          n.sub.8 = 1.6968                                                                          ν.sub.8 = 56.5                                       r.sub.14 = 47.6                                                                         d.sub.14 = 20.5                                                     r.sub.15 = 455.8                                                                        filter thickness 4.3                                           L.sub.9        d.sub.15 = 10.3                                                                           n.sub.9 = 1.8051                                                                      ν.sub.9 = 25.4                                .sub.16 =-249.8                                                                        d.sub.16 = 9.9                                                      r.sub.17 =-834.6                                                         L.sub.10       d.sub.17 = 57.2                                                                           n.sub.10 = 1.4645                                                                     ν.sub.10 = 66.0                              r.sub.18 =-66.9                                                                         d.sub.18 = 0.5                                                      r.sub.19 =-201.9                                                         L.sub.11       d.sub.19 = 5.4                                                                            n.sub.11 = 1.8051                                                                     ν.sub.11 = 25.4                              r.sub.20 = 157.9                                                                        d.sub.20 = 11.1                                                     r.sub.21 =-1167.6                                                        L.sub.12       d.sub.21 = 25.5                                                                           n.sub.12 = 1.4645                                                                     ν.sub.12 = 66.0                              r.sub.22 =-95.6                                                                         d.sub.22 = 0.5                                                      r.sub.23 = 10629.3                                                       L.sub.13       d.sub.23 = 18.9                                                                           n.sub.13 = 1.6204                                                                     ν.sub.13 = 60.3                              r.sub.24 =-209.0                                                         __________________________________________________________________________

FIG. 2a shows the spherical aberration and sine condition, FIG. 2b showsthe chromatic aberration, FIG. 2c shows the distortion, and FIG. 2dshows the astigmatism of the lens system shown in FIG. 1 and defined inTable 1.

The second example is shown in FIG. 3 and consists of first and secondnegative meniscus lenses L₁ and L₂ convex to the object, a positive lensL₃, a negative meniscus lens L₄ which, like lenses L₁ and L₂, is convexto the object, a cemented triplet consisting of negative lenses L₅ andL₇ cemented to opposite surfaces of a biconvex lens L₆, a negativemeniscus lens L₈ convex to the object, a positive lens L₉, acomparatively thick positive lens L₁₀, a negative lens L₁₁ and positivemeniscus lenses L₁₂ and L₁₃ both of which are convex to the image. Afilter is located between lenses L₈ and L₉, although again the positionof the filter is not critical. The radii r₁ to r₂₄ and the thicknessesand separations d₁ to d₂₃, along with the refractive indices n₁ to n₁₃and Abbe numbers ν₁ to ν ₁₃ for lenses L₁ to L₁₃ are given in Table 2 asfollows:

F = 100

F₁.2 =-161.8

F₁.2.3 = -407.1

f₆ = 80.6

                                      TABLE 2                                     __________________________________________________________________________         Radius of Curva-                                                                        Lens Thickness                                                                            Refractive                                                                            Abbe                                       Lens ture r    or Distance d                                                                             Index n No. ν                                   __________________________________________________________________________         r.sub.1 = 234.4                                                          L.sub.1                                                                                      d.sub.1 = 6.5                                                                             n.sub.1 = 1.6031                                                                      ν.sub.1 = 60.7                               r.sub.2 = 115.9                                                                         d.sub.2 = 48.9                                                      r.sub.3 = 281.5                                                          L.sub.2                                                                                      d.sub.3 = 14.1                                                                            n.sub.2 = 1.7340                                                                      ν.sub.2 = 51.5                               r.sub.4 = 121.9                                                                         d.sub.4 = 56.5                                                      r.sub.5 = 600.7                                                          L.sub.3                                                                                      d.sub.5 = 27.6                                                                            n.sub.3 = 1.6200                                                                      ν.sub.3 = 36.3                               r.sub.6 =-416.3                                                                         d.sub.6 = 7.1                                                       r.sub.7 = 205.1                                                          L.sub.4                                                                                      d.sub.7 = 9.3                                                                             n.sub.4 = 1.7995                                                                      ν.sub.4 =  42.2                              r.sub.8 = 129.4                                                                         d.sub.8 = 14.5                                                      r.sub.9 = 280.4                                                          L.sub.5                                                                                      d.sub.9 = 8.1                                                                             n.sub.5 = 1.5523                                                                      ν.sub.5 = 63.7                               r.sub.10 = 111.9                                                         L.sub.6                                                                                      d.sub.10 = 42.1                                                                           n.sub.6 = 1.7200                                                                      ν.sub.6 = 50.3                               r.sub.11 =-101.4                                                         L.sub.7                                                                                      d.sub.11 = 12.6                                                                           n.sub.7 = 1.5613                                                                      ν.sub.7 = 45.2                               r.sub.12 =-13184.4                                                                      d.sub.12 = 0.5                                                      r.sub.13 = 102.0                                                         L.sub.8                                                                                      d.sub.13 = 6.4                                                                            n.sub.8 = 1.7200                                                                      ν.sub.8 = 50.3                               r.sub.14 = 47.5                                                                         d.sub.14 = 16.9                                                               filter thickness 4.3                                                r.sub.15 = 485.3                                                         L.sub.9                                                                                      d.sub.15 = 11.7                                                                           n.sub.9 = 1.8051                                                                      ν.sub.9 =  25.4                              r.sub.16 =-264.1                                                                        d.sub.16 = 9.9                                                      r.sub.17 =-5686.1                                                        L.sub.10                                                                                     d.sub.17 = 62.1                                                                           n.sub.10 = 1.4645                                                                     ν.sub.10 = 66.0                              r.sub.18 =-66.7                                                                         d.sub.18 = 0.5                                                      r.sub.19 =-273.7                                                         L.sub.11                                                                                     d.sub.19 = 6.5                                                                            n.sub.11 = 1.8051                                                                     ν.sub.11 = 25.4                              r.sub.20 = 151.0                                                                        d.sub.20 = 14.6                                                     r.sub.21 =-725.0                                                         L.sub.12                                                                                     d.sub.21 = 23.4                                                                           n.sub.12 = 1.4645                                                                     ν.sub.12 = 66.0                              r.sub.22 =-100.0                                                                        d.sub.22 = 0.5                                                      r.sub.23 =-3616.9                                                        L.sub.13                                                                                     d.sub.23 = 18.7                                                                           n.sub.13 = 1.6204                                                                     ν.sub.13 = 60.3                              r.sub.24 =-200.9                                                         __________________________________________________________________________

FIG. 4a shows the spherical aberration and sine condition, FIG. 4b showsthe chromatic aberration. FIG. 4c shows the distortion, and FIG. 4dshows the astigmatism of the lens system shown in FIG. 3 and defined inTable 2.

It will be apparent that the embodiments shown are only exemplary andthat various modifications can be made in construction and arrangementwithin the scope of the invention as defined in the appended claims.

What is claimed is:
 1. A super wide angle lens comprising 13 lensesgrouped in 11 components wherein the first and second lenses arenegative meniscus lenses convex to the object, the third lens is apositive lens, the fourth lens is a negative meniscus lens convex to theobject, the fifth, sixth and seventh lenses constitute a cementedtriplet, the eighth lens is a negative meniscus lens convex to theobject, the ninth lens is a positive lens, the tenth lens is a thickpositive lens, the eleventh lens is a negative lens, and the twelfth andthirteenth lenses are positive lenses convex to the image, and furthercomprising a filter located between said eighth and ninth lenses,wherein the radii r₁ to r₂₄, the thickness and separations d₁ to d₂₃,the refractive indices n₁ to n₁₃, and Abbe numbers ν₁ to ν₁₃ of saidfirst to thirteen lenses L₁ to L₁₃, respectively, satisfy the followingconditions:

         Radius of  Lens Thick- Refractive                                                                             Abbe                                                     ness or                                                       Lens Curvature r                                                                              or Distance d                                                                             Index n  No. ν                                 ______________________________________                                             r.sub.1 = 256.3                                                          L.sub.1         d.sub.1 = 6.5                                                                             n.sub.1 = 1.6031                                                                       ν.sub.1 = 60.7                             r.sub.2 = 121.6                                                                          d.sub.2 = 47.4                                                     r.sub.3 = 253.9                                                          L.sub.2         d.sub.3 = 14.1                                                                            n.sub.2 = 1.7410                                                                       ν.sub.2 = 52.7                             r.sub.4 = 125.8                                                                          d.sub.4 = 57.4                                                     r.sub.5 = 783.8                                                          L.sub.3         d.sub.5 = 22.9                                                                            n.sub.3 = 1.6258                                                                       ν.sub.3 = 35.7                             r.sub.6 =-430.9                                                                          d.sub.6 = 6.1                                                      r.sub.7 = 211.3                                                          L.sub.4         d.sub.7 = 9.3                                                                             n.sub.4 = 1.8160                                                                       ν.sub.4 = 46.8                             r.sub.8 = 119.7                                                                          d.sub.8 = 16.4                                                     r.sub.9 = 277.8                                                          L.sub.5         d.sub.9 = 8.1                                                                             n.sub.5 = 1.5473                                                                       ν.sub.5 = 53.6                             r.sub.10 = 119.3                                                         L.sub.6         d.sub.10 = 43.2                                                                           n.sub.6 = 1.7200                                                                       ν.sub.6 = 50.3                             r.sub.11 =-100.4                                                         L.sub.7         d.sub.11 = 12.6                                                                           n.sub.7 = 1.5613                                                                       ν.sub.7 = 45.2                             r.sub.12 = 5113.5                                                                        d.sub.12 = 0.5                                                     r.sub.13 = 89.6                                                          L.sub.8         d.sub.13 = 8.1                                                                            n.sub.8 = 1.6968                                                                       ν.sub.8 = 56.5                             r.sub.14 = 47.6                                                                          d.sub.14 = 20.5                                                    r.sub.15 = 455.8                                                                         filter thickness                                                              4.3                                                           L.sub.9         d.sub.15 = 10.3                                                                           n.sub.9 = 1.8051                                                                       ν.sub.9 = 25.4                             r.sub.16 =-249.8                                                                         d.sub.16 = 9.9                                                     r.sub.17 =-834.6                                                         L.sub.10        d.sub.17 = 57.2                                                                           n.sub.10 = 1.4645                                                                      ν.sub.10 = 66.0                            r.sub.18 =-66.9                                                                          d.sub.18 = 0.5                                                     r.sub.19 =-201.9                                                         L.sub.11        d.sub.19 = 5.4                                                                            n.sub.11 = 1.8051                                                                      ν.sub.11 = 25.4                            r.sub.20 = 157.9                                                                         d.sub.20 = 11.1                                                    r.sub.21 =-1167.6                                                        L.sub.12        d.sub.21 = 25.5                                                                           n.sub.12 = 1.4645                                                                      ν.sub.12 = 66.0                            r.sub.22 =-95.6                                                               d.sub.22 = 0.5                                                                r.sub.23 = 10629.3                                                       L.sub.13        d.sub.23 = 18.9                                                                           n.sub.13 = 1.6204                                                                      ν.sub.13 = 60.3                            r.sub.24 =-209.0                                                         ______________________________________                                    


2. A super wide angle lens comprising thirteen lenses grouped in elevencomponents wherein the first and second lenses are negative meniscuslenses convex to the object, the third lens is a positive lens, thefourth lens is a negative meniscus lens convex to the object, the fifth,sixth and seventh lenses constitute a cemented triplet, the eighth lensis a negative meniscus lens convex to the object, the ninth lens is apositive lens, the tenth lens is a thick positive lens, the eleventhlens is a negative lens, and the twelfth and thirteenth lenses arepositive lenses convex to the image, and further comprising a filterlocated between said eighth and ninth lenses, wherein the radii r₁ tor₂₄, the thicknesses and separations d₁ to d₂₃, the refractive indicesn₁ to n₁₃, and Abbe numbers ν₁ to ν₁₃ of said first to thirteenth lensesL₁ to L₁₃, respectively, satisfy the following conditions:

         Radius of Curva-                                                                        Lens Thickness                                                                            Refractive                                                                            Abbe                                       Lens ture r    or Distance d                                                                             Index n No. ν                                   __________________________________________________________________________         r.sub.1 = 234.4                                                          L.sub.1                                                                                      d.sub.1 = 6.5                                                                             n.sub.1 = 1.6031                                                                      ν.sub.1 = 60.7                               r.sub.2 = 115.9                                                                         d.sub.2 = 48.9                                                      r.sub.3 = 281.5                                                          L.sub.2                                                                                      d.sub.3 = 14.1                                                                            n.sub.2 = 1.7340                                                                      ν.sub.2 = 51.51- r.sub.4 = 121.9                       d.sub.4 = 56.5                                                      r.sub.5 = 600.7                                                          L.sub.3                                                                                      d.sub.5 = 27.6                                                                            n.sub.3 = 1.6200                                                                      ν.sub.3 = 36.3                               r.sub.6 =-416.3                                                                         d.sub.6 = 7.1                                                       r.sub.7 = 205.1                                                          L.sub.4                                                                                      d.sub.7 = 9.3                                                                             n.sub.4 = 1.7995                                                                      ν.sub.4 = 42.2                               r.sub.8 = 129.4                                                                         d.sub.8 = 14.5                                                      r.sub.9 = 280.4                                                          L.sub.5                                                                                      d.sub.9 = 8.1                                                                             n.sub.5 = 1.5523                                                                      ν.sub.5 = 63.7                               r.sub.10 = 111.9                                                         L.sub.6                                                                                      d.sub.10 = 42.1                                                                           n.sub.6 = 1.7200                                                                      ν.sub.6 = 50.3                               r.sub.11 =-101.4                                                         Lhd 7                                                                                        d.sub.11 = 12.6                                                                           n.sub.7 = 1.5613                                                                      ν.sub.7 = 45.2                               r.sub.12 =-13184.4                                                                      d.sub.12 = 0.5                                                      r.sub.13 = 102.0                                                         L.sub.8                                                                                      d.sub.13 = 6.4                                                                            n.sub.8 = 1.7200                                                                      ν.sub.8 = 50.3                               r.sub.14 = 47.5                                                                         d.sub.14 = 16.9                                                     r.sub.15 = 485.3                                                                        filter thickness 4.3                                           L.sub.9                                                                                      d.sub.15 = 11.7                                                                           n.sub.9 = 1.8051                                                                      ν.sub.9 = 25.4                               r.sub.16 =-264.1                                                                        d.sub. 16 = 9.9                                                     r.sub.17 =-5686.1                                                        L.sub.10                                                                                     d.sub.17 = 62.1                                                                           n.sub.10 = 1.4645                                                                     ν.sub.10 = 66.0                              r.sub.18 =-66.7                                                                         d.sub.18 = 0.5                                                      r.sub.19 =-273.7                                                         L.sub.11                                                                                     d.sub.19 = 6.5                                                                            n.sub.11 = 1.8051                                                                     ν.sub.11 = 25.4                              r.sub.20 = 151.0                                                                        d.sub.20 = 14.6                                                     r.sub.21 =-725.0                                                         L.sub.12                                                                                     d.sub.21 = 23.4                                                                           n.sub.12 = 1.4645                                                                     ν.sub.12 = 66.0                              r.sub.22 =-100.0                                                                        d.sub.22 = 0.5                                                      r.sub.23 =-3616.9                                                        L.sub.13                                                                                     d.sub.23 = 18.7                                                                           n.sub.13 = 1.6204                                                                     ν.sub.13 = 60.3                              r.sub.24 =-200.9.                                                        __________________________________________________________________________